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In this paper we prove a lower bound of Ω(n log n) for the common element problem on two sets of size n each. Two interesting consequences of this lower bound are also discussed. In particular, we show that linear space neural network models that admit unbalanced rules cannot draw all inferences in time independent of the knowledge base size. We also show that the join operation in data base applications needs Ω(log n) time given only n processors.
Paul Dietz, Danny Krizanc, Sanguthevar Rajasekaran, and Lokendra Shastri, "A Lower Bound Result for the Common Element Problem and Its Implication for Reflexive Reasoning", . August 1993.
Date Posted: 21 August 2007